Rotational Mechanics
AdvancedRotational mechanics extends Newtonian dynamics to spinning and rolling objects using calculus. Torque drives angular acceleration through tau = I alpha.
Moment of inertia is computed by integrating r^2 dm. Angular momentum L = I omega is conserved when no external torque acts.
Rolling without slipping couples translation and rotation through v = R omega.
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Learning objectives
- •Relate angular position, velocity, and acceleration using calculus
- •Calculate torque and apply the rotational second law
- •Derive moment of inertia using integration
- •Apply the parallel axis theorem
- •Apply conservation of angular momentum
- •Analyze rolling-without-slipping motion
Recommended Resources
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Books
Classical Mechanics
by John R. Taylor
An Introduction to Mechanics
by Daniel Kleppner and Robert Kolenkow
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